57.3.1 problem 1

Internal problem ID [9058]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 1
Date solved : Sunday, March 30, 2025 at 02:05:54 PM
CAS classification : [_linear]

\begin{align*} t y^{\prime }+y&=t \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=5 \end{align*}

✓ Maple. Time used: 0.104 (sec). Leaf size: 16

ode:=t*diff(y(t),t)+y(t) = t; 
ic:=y(0) = 5; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \frac {5 \delta \left (t \right )}{\delta \left (0\right )}+\frac {t}{2} \]

✗ Mathematica

ode=t*D[y[t],t]+y[t]==t; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✓ Sympy. Time used: 0.168 (sec). Leaf size: 5

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) - t + y(t),0) 
ics = {y(0): 5} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {t}{2} \]